Approximate controllability for fractional diffusion equations by interior control

We consider the approximate controllability by interior control of a partial differential equation with time derivatives of non-integer order. First, we prove the well-posedness of the inhomogeneous problem for the controlled system. Next, we study the dual system and show a weak type of unique continuation property. Finally, we prove the approximate controllability.     

Finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay via periodically intermittent control

In this paper, the issue of finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay (CRDSTD) is considered. A periodically intermittent controller is designed such that drive system and corresponding response system can achieve finite-time lag synchronization. By using graph theory and Lyapunov method, two sufficient criteria are presented to guarantee the finite-time lag synchronization of CRDSTD. Moreover, the time of achieving lag synchronization of CRDSTD is estimated. Finally, a numerical example is given to show the effectiveness of the proposed results.     

A Multilevel Event History Model of Social Diffusion: Medical Innovation Revisited

This article presents a multilevel event history model of social diffusion and applies it to Coleman, Katz, and Menzel's (1966 Coleman , J. S. , Katz , E. , &; Menzel , H. ( 1966 ). Medical Innovation: A Diffusion Study . Indianapolis , IN : Bobbs-Merrill . [Google Scholar]) data on the adoption of tetracycline by physicians. The simplest form of a multilevel model allows a random intercept. In the present application of this simple model to the Medical Innovation data, structured for an event history analysis, the physicians are nested in city and time. Random intercepts capture effects of contextual conditions that are shared by event history cases with the same city–time status. The intercepts also reflect any baseline internal contagion effects, that is, the proportion of physicians in the city–time network who have adopted the drug at time t ? 1. Here, I show that Van den Bulte and Lilien's (2001 Van den Bulte , C. &; Lilien , G. L. ( 2001 ). Medical innovation revisited: social contagion versus marketing effort . American Journal of Sociology , 106 , 1409 – 1435 .[Crossref], [Web of Science ®] , [Google Scholar]) finding of an important contextual effect of drug firms' marketing effort is misleading. I also show that the social network in which physicians are situated significantly contributes to their adoptions, controlling for baseline internal contagion effects and individual-level characteristics of physicians, which have been emphasized in investigations of these data.     

Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids

A diffusion driven model for hepatitis B virus (HBV) infection, taking into account the spatial mobility of both the HBV and the HBV DNA-containing capsids is presented. The global stability for the continuous model is discussed in terms of the basic reproduction number. The analysis is further carried out on a discretized version of the model. Since the standard finite difference (SFD) approximation could potentially lead to numerical instability, it has to be restricted or eliminated through dynamic consistency. The latter is accomplished by using a non-standard finite difference (NSFD) scheme and the global stability properties of the discretized model are studied. The results are numerically illustrated for the dynamics and stability of the various populations in addition to demonstrating the advantages of the usage of NSFD method over the SFD scheme.     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.     

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

Let X(1)= {X(1)(s), s ∈ R+ } and X(2)= {X(2)(t), t ∈ R+ } be two independent nondegenerate diusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1)and X(2)are studied. More generally, let E1, E2 ■(0, ∞) and F  Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1) ∩ X(2)(E2) ∩ F = φ} 0 are proved in terms of the Bessel-Riesz type capacity and Hausdor measure of E1 ×E2 ×F in the metric space(R+ ×R+ ×Rd, ρ), where ρ is an unsymmetric metric defined in R+ × R+ × Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.     

Electrical characteristics of thin Ni2Si,NiSi, and NiSi2 layers grown on silicon

We have determined the resistivity, carrier concentration, and Hall mobility as a function of thickness (700–3000 Å) of Ni₂Si, NiSi, and NiSi₂ layers formed by vacuum annealing at 270÷v300°C, ≈ 400°C, and ≈ 800°C, respectively, of nickel films vacuum-deposited on a silicon substrate (111 n-type and 100 p-type Si ρ ≈ 1KΩ). The layer thicknesses were measured by 2 MeV⁴He⁺ backscattering spectrometry. The silicide phase was confirmed by x-ray measurements. The electrical measurements were carried out using van der Pauw configuration. We found the electrical transport parameters to be independent of the film thickness within the experimental uncertainty. The Hall factors were assumed to be unity. The majority carriers are electrons in NiSi and holes in Ni₂Si and NiSi₂. The resistivity values are 24±2, 14±1, and 34±2 μΩcm, the electron concentrations are 9±3, 10 and 7±1, and ≈ 2 × 10²² cm^?3, and the Hall mobilities are 3±1, ≈ 4.5 and 6, and ≈ 9 cm²/Vs for Ni₂Si, NiSi (〈100〉 and 〈111〉), and NiSi₂, respectively. The systematic error in the measured values caused by currents in the high resistivity substrate is estimated to be less than 6% for the Hall coefficient. The results show that Ni₂Si, NiSi, and NiSi₂ layers formed by a thin film reaction are electrically metallic conductors, a result which concurs with those reported previously (1) for refractory metal silicides. The Hall mobility increases with the Si content in the silicide. The electron concentration is lowest for NiSi₂ leading to the highest resistivity for the epitaxial phase of NiSi₂.     

扩散方程基本解的积分处理

详细讨论了时间相关热交换问题扩散方程基本解的时间积分特性，给出了完整的解析处理及相应级数展开表达式，并提出采用按时段构造的时间单元局部化基本解作为边界元法的加权函数，从而显著减少可动边界问题边界元解法的存贮量和计算时间。     

Surface diffusion of metal atoms on polymer substrates during physical vapour deposition

 The surface diffusion of physical-vapour-deposited metal atoms on thermoplastic polymer substrates was investigated. In accordance with the hypothesis of the “classical” atomistic diffusion model, diffusion coefficients are derived from a Monte Carlo simulation. Because the “classical” atomistic diffusion model neglects the desorption of the metal atoms, the absolute diffusion data obtained in our investigations should only be considered as rough estimates. It is more the intention of our work to present relative values in order to correlate the metal surface diffusion on polymer substrates with their physical states (morphologies and surface dynamics). As expected, the diffusivity of metal atoms is strongly influenced by the chemical affinity (“reactivity”) between the metal atoms and the polymer substrate. Furthermore, the diffusivity strongly depends on the physical state of the polymer substrate. On polymer surfaces above the glass-transition temperature the surface diffusivity of metal atoms is 1 order of magnitude higher than the diffusivity below the glass-transition temperature. Received: 9 April 1999/Accepted in revised form: 21 October 1999